The angle of incidence of the light beam on a plane-parallel glass plate 12 mm thick is 60°. How much did the light beam move when it passed through the plate?
Question
The angle of incidence of the light beam on a plane-parallel glass plate 12 mm thick is 60°. How much did the light beam move when it passed through the plate?
Solution
To solve this problem, we need to use the laws of refraction, also known as Snell's law.
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First, we need to find the angle of refraction. The refractive index of glass is typically around 1.5. Using Snell's law, we have:
n1 * sin(i) = n2 * sin(r)
Where n1 is the refractive index of air (approximately 1), i is the angle of incidence (60°), n2 is the refractive index of glass, and r is the angle of refraction. Solving for r gives:
r = arcsin[(n1/n2) * sin(i)] r = arcsin[(1/1.5) * sin(60°)] r = arcsin(0.577) ≈ 35.3°
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Next, we need to find the lateral displacement of the light beam. This can be found using the formula:
d = t * tan(i - r)
Where d is the lateral displacement, t is the thickness of the glass plate (12 mm), i is the angle of incidence, and r is the angle of refraction. Substituting the known values gives:
d = 12mm * tan(60° - 35.3°) d = 12mm * tan(24.7°) d = 12mm * 0.465 d = 5.58 mm
So, the light beam moved approximately 5.58 mm when it passed through the plate.
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